Multiscaling and clustering of volatility

The dynamics of prices in stock markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, while the distribution of returns of the most important indices is known to be a truncated Lévy, the behaviour of volatility correlations is still poorly understood. What is well known is that absolute returns have memory on a long time range, this phenomenon is known in financial literature as clustering of volatility. In this paper we show that volatility correlations are power laws with a non-unique scaling exponent. This kind of multiscale phenomenology is known to be relevant in fully developed turbulence and in disordered systems and it is pointed out here for the first time for a financial series. In our study we consider the New York Stock Exchange (NYSE) daily index, from January 1966 to June 1998, for a total of 8180 working days.